From Kepler's Law we know, #T^2 prop r^3#
So, #T^2 = K r^3#(let, #K# is a constant)
Now,we know, #V=omega r = (2pi)/ T *r#
So, #T=(2pi)/V *r#
So, #4 pi^2 r^2 / V^2 = K r^3#
Now,multiplying both side by #m# and rearranging to write,
#(mV^2) / r^2 =1/K (4 pi^2m)/r^3#
Multiplying both side by #r#,we get,
#(mV^2)/r = ((4pi^2)/K)m/r^2= C m/r^2#
So, #(mV^2)/r# is the required centripetal force for a planet to move round the Sun i,e the attractive force or the gravitational force acting in between the planet of mass #m# and radius of orbit #r#
So, we can write, #F= C m/r^2# (where, #C# is a constant)
This is the Newton's Law of gravitation.
In reality #C= GM# (where, #G# is the gravitational constant and #M# is the mass of sun)
